Question

A die is thrown 100 times. Getting an even number is considered a success. The variance of the number of successes is

• A. 20
• B. 25
• C. 30
• D. 50

Hint:

For binomial distribution: Variance = \(npq\).
Here \(p = \frac{1}{2}\) for even numbers on a die.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a binomial distribution problem.
Each throw is a trial with success probability \(p\).

Step 2: Key Formula or Approach:
Variance of binomial distribution = \(npq\).

Step 3: Detailed Explanation:
On a die, the probability of getting an even number (2, 4, 6) is \(p = \frac{3}{6} = 0.5\).
Number of trials \(n = 100\).
So \(q = 1 - p = 0.5\).
Variance = \(npq = 100 \times 0.5 \times 0.5 = 25\).
Thus, the variance is 25, which is option (B).
The standard deviation would be \(\sqrt{25} = 5\).
Binomial distribution is appropriate here because each throw is independent.